Give reason to show that none of the numbers, given below, is a perfect square.
(i) `2162`
(ii) `6843`
(iii) `9637`
(iv) `6598`

Answer

To determine whether the given numbers are perfect squares, we will analyze the unit digits of each number. A perfect square can only end with certain digits: 0, 1, 4, 5, 6, or 9. If the unit digit of a number is not one of these, then the number cannot be a perfect square.

Let's analyze each number step by step:

### Step 1: Analyze the first number `2162`
- **Unit digit**: The unit digit of `2162` is `2`.
- **Check**: Since `2` is not in the list of possible unit digits for perfect squares (0, 1, 4, 5, 6, 9), `2162` is not a perfect square.

### Step 2: Analyze the second number `6843`
- **Unit digit**: The unit digit of `6843` is `3`.
- **Check**: Since `3` is not in the list of possible unit digits for perfect squares, `6843` is not a perfect square.

### Step 3: Analyze the third number `9637`
- **Unit digit**: The unit digit of `9637` is `7`.
- **Check**: Since `7` is not in the list of possible unit digits for perfect squares, `9637` is not a perfect square.

### Step 4: Analyze the fourth number `6598`
- **Unit digit**: The unit digit of `6598` is `8`.
- **Check**: Since `8` is not in the list of possible unit digits for perfect squares, `6598` is not a perfect square.

### Conclusion
None of the numbers `2162`, `6843`, `9637`, and `6598` are perfect squares because their unit digits (2, 3, 7, and 8 respectively) do not match the unit digits that can be found in perfect squares (0, 1, 4, 5, 6, 9).

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